The solubility of electrolytes `MX_(1),MX_(2) and MX_(3) is 1xx10^(-3)` moles per litre. Hence their respective solubility products are :

Options

A. `10xx^(-6), 4xx10^(-9), 27xx10^(-12)`
B. `10^(-9), 4xx10^(-9), 32xx10^(-12)`
C. `10^(-9), 8xx10^(-8), 32xx10^(-12)`
D. None of these

Answer

To find the solubility products of the electrolytes MX1, MX2, and MX3, we will follow these steps:

### Step 1: Determine the dissociation of MX1
For the electrolyte MX1, let's assume it dissociates as follows:
\[ MX_1 \rightleftharpoons M^+ + X^- \]
If the solubility of MX1 is \( s = 1 \times 10^{-3} \) moles per liter, then at equilibrium:
- The concentration of \( M^+ \) = \( s \)
- The concentration of \( X^- \) = \( s \)

### Step 2: Write the expression for the solubility product (Ksp) of MX1
The solubility product \( K_{sp} \) is given by:
\[ K_{sp} = [M^+][X^-] = s \cdot s = s^2 \]
Substituting the value of \( s \):
\[ K_{sp} = (1 \times 10^{-3})^2 = 1 \times 10^{-6} \]

### Step 3: Determine the dissociation of MX2
For the electrolyte MX2, it dissociates as:
\[ MX_2 \rightleftharpoons M^{2+} + 2X^- \]
At equilibrium, if the solubility is \( s = 1 \times 10^{-3} \):
- The concentration of \( M^{2+} \) = \( s \)
- The concentration of \( X^- \) = \( 2s \)

### Step 4: Write the expression for the solubility product (Ksp) of MX2
The solubility product \( K_{sp} \) is given by:
\[ K_{sp} = [M^{2+}][X^-]^2 = s \cdot (2s)^2 = s \cdot 4s^2 = 4s^3 \]
Substituting the value of \( s \):
\[ K_{sp} = 4(1 \times 10^{-3})^3 = 4 \times 10^{-9} \]

### Step 5: Determine the dissociation of MX3
For the electrolyte MX3, it dissociates as:
\[ MX_3 \rightleftharpoons M^{3+} + 3X^- \]
At equilibrium, if the solubility is \( s = 1 \times 10^{-3} \):
- The concentration of \( M^{3+} \) = \( s \)
- The concentration of \( X^- \) = \( 3s \)

### Step 6: Write the expression for the solubility product (Ksp) of MX3
The solubility product \( K_{sp} \) is given by:
\[ K_{sp} = [M^{3+}][X^-]^3 = s \cdot (3s)^3 = s \cdot 27s^3 = 27s^4 \]
Substituting the value of \( s \):
\[ K_{sp} = 27(1 \times 10^{-3})^4 = 27 \times 10^{-12} \]

### Summary of Results
- The solubility product of MX1 is \( 1 \times 10^{-6} \)
- The solubility product of MX2 is \( 4 \times 10^{-9} \)
- The solubility product of MX3 is \( 27 \times 10^{-12} \)